Pith Number

pith:OJRN5GG4

pith:2021:OJRN5GG4TY6TQFTACZ7TSKW7RB

not attested not anchored not stored refs pending

Realization problems of graphs as Reeb graphs of Morse functions with prescribed preimages

Naoki Kitazawa

arxiv:2108.06913 v4 · 2021-08-16 · math.GN · math.GT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OJRN5GG4TY6TQFTACZ7TSKW7RB}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Cited by

3 papers in Pith

Representations of Reeb spaces via simplified graphs and examples

Morse functions with regular level sets consisting of $2$-dimensional spheres, $2$-dimensional tori, or Klein Bottles

Receipt and verification

First computed	2026-07-05T06:21:02.980324Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7262de98dc9e3d381660167f392adf887ebc65db6303700b9eaf38fc5f80786b

Aliases

arxiv: 2108.06913 · arxiv_version: 2108.06913v4 · doi: 10.48550/arxiv.2108.06913 · pith_short_12: OJRN5GG4TY6T · pith_short_16: OJRN5GG4TY6TQFTA · pith_short_8: OJRN5GG4

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/OJRN5GG4TY6TQFTACZ7TSKW7RB \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 7262de98dc9e3d381660167f392adf887ebc65db6303700b9eaf38fc5f80786b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "630dbac6b551b47e0f740377dd6614f104a96974a7a8d6bc7015e1cf314c0b1d",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GN",
    "submitted_at": "2021-08-16T06:17:58Z",
    "title_canon_sha256": "92c86db0ae4e254796fa3d8bf7c7612bd6f8d513098ff5235c0ea18224f22da9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2108.06913",
    "kind": "arxiv",
    "version": 4
  }
}